A. Alfred Taubman's shopping mall empire plans to sell shares to the public, hoping to raise between $335 million and $389 million from investors who would get a 22 percent stake in a group of 19 large shopping malls from California to Connecticut, the company announced yesterday.

The move would effectively free Mr. Taubman of hundreds of millions of dollars of personal debt.

The company said the offering and the accompanying restructuring would enable it to slash debt and expand.

It said it planned to enlarge some large regional shopping centers and might buy or build others.

Mr. Taubman, a 67-year-old real estate developer who controls Sotheby's Holdings as well as the Woodward & Lothrop department store chain based in Washington, would end up owning less of his shopping center empire than the public would.

The plan is to ask the public to pay more than 50 times last year's earnings for a stake in the company.

The success of the deal will hinge on the willingness of investors to pay such a high multiple. If the offering of 26.8 million shares goes as planned, with shares selling at $13.50 each, the %J midpoint of the $12.50 to $14.50 range in the prospectus, the General Motors and AT&T pension funds would end up with $327 million in cash and equity interests worth $874 million.

Mr. Taubman would own a stake worth about $326 million, although he has pledged that holding to banks in return for $80 million in loans.

The Taubman properties include a 1.9-million-square-foot Woodfield Mall in Schaumburg, Ill. Other shopping centers are in Michigan, Virginia, Ohio, California, New Jersey, Maryland (Marley Station), Connecticut, Colorado and Tennessee.